4. B modeling#

4.1. Characteristics of modeling#

We use a AXIS model.

In this case, the coefficient \({K}_{D}\) is chosen depending on the temperature and on \({\sigma }_{0}\).

T (°C)

0 MPa

100 MPa

200

200 MPa

900

14,355

14,855

15,355

1000

14.5

15

15.5

1025

14.5363

15.0363

15.5363

15.5363

1050

14.5725

15.0725

15.5725

15.5725

Table 4.1-1 : K_D of B modeling

The discretization in time is quite fine:

(JUSQU_A = 2, NOMBRE = 10),

(JUSQU_A = 2., NOMBRE = 10),

(JUSQU_A = 20., NOMBRE = 10),

(JUSQU_A = 200., NOMBRE = 10),

(JUSQU_A = 2000., NOMBRE = 10),

(JUSQU_A = 20000., NOMBRE = 10),

(JUSQU_A = 200,000., NOMBRE = 10),

(JUSQU_A = 1000000., NOMBRE = 30),

(JUSQU_A = 1600000., NOMBRE = 30),

(JUSQU_A = 1700000., NOMBRE = 40),

(JUSQU_A = 1800000., NOMBRE = 40),

(JUSQU_A = 1900000., NOMBRE = 40),

(JUSQU_A = 2000000., NOMBRE = 40),

(JUSQU_A = 2100000., NOMBRE = 40),

(JUSQU_A = 2200000., NOMBRE = 40),

(JUSQU_A = 2300000., NOMBRE = 40),

(JUSQU_A = 2400000., NOMBRE = 40),

(JUSQU_A = 2500000., NOMBRE = 40),

4.2. Characteristics of the mesh#

It is chosen to represent the cylindrical test piece by a quadrangle with 8 knots in axisymmetry.

Number of knots: 8

Number of stitches: 1 (QUAD8)

_images/10000201000001BD0000022CAEC440B46B4E3C28.png

Image 4.2-1: Modeling B mesh

4.3. Tested sizes and results#

Evolution of the constraint, \({\sigma }_{0}\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

75.97849999999999997

0.5

1600000

“ANALYTIQUE”

55.54209999999999998

10.0

Table 4.3-1 : B modeling results**

Evolution of the damage variable, \(D\) as a function of time. This value is tested at various times depending on the modeling:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

0.110134

1.0

1600000

“ANALYTIQUE”

0.28131600000000001

10.0

Table 4.3-2 : B modeling results

Evolution of the viscoplastic isotropic work hardening variable, \(r\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

2.747799999999999999E-3

0.5

1600000

“ANALYTIQUE”

2.79276E-3

0.5

Table 4.3-3 : B modeling results

Evolution of the viscoplastic isotropic work hardening variable, \(p\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

2.7607899999999999E-3

0.5

1600000

“ANALYTIQUE”

2.814779999999999998E-3

0.5

Table 4.3-4 : B modeling results**